“Amy is thrilled to be nominated for 6 Grammys and is very much hoping to attend,” her rep tells PEOPLE. “She is determined to be ready and well for that performance.”

The 24-year-old singer – whose husband Blake Fielder-Civil is in jail – last month canceled her appearances for the rest of the year. She’s currently in a program being supervised by doctors – and, her rep said, writing a lot. “It’s a really difficult time and she’s been channeling it into her music.”

For more on Winehouse’s struggles and her rise to fame, pick up the latest PEOPLE, on newsstands now